| SSweibull | R Documentation |
This selfStart model evaluates the Weibull model for growth
curve data and its gradient. It has an initial attribute that
will evaluate initial estimates of the parameters Asym, Drop,
lrc, and pwr for a given set of data.
SSweibull(x, Asym, Drop, lrc, pwr)
x |
a numeric vector of values at which to evaluate the model. |
Asym |
a numeric parameter representing the horizontal asymptote on
the right side (very small values of |
Drop |
a numeric parameter representing the change from
|
lrc |
a numeric parameter representing the natural logarithm of the rate constant. |
pwr |
a numeric parameter representing the power to which |
This model is a generalization of the SSasymp model in
that it reduces to SSasymp when pwr is unity.
a numeric vector of the same length as x. It is the value of
the expression Asym-Drop*exp(-exp(lrc)*x^pwr). If all of
the arguments Asym, Drop, lrc, and pwr are
names of objects, the gradient matrix with respect to these names is
attached as an attribute named gradient.
Douglas Bates
Ratkowsky, David A. (1983), Nonlinear Regression Modeling, Dekker. (section 4.4.5)
nls, selfStart, SSasymp
Chick.6 <- subset(ChickWeight, (Chick == 6) & (Time > 0))
SSweibull(Chick.6$Time, 160, 115, -5.5, 2.5) # response only
local({ Asym <- 160; Drop <- 115; lrc <- -5.5; pwr <- 2.5
SSweibull(Chick.6$Time, Asym, Drop, lrc, pwr) # response _and_ gradient
})
## IGNORE_RDIFF_BEGIN
getInitial(weight ~ SSweibull(Time, Asym, Drop, lrc, pwr), data = Chick.6)
## IGNORE_RDIFF_END
## Initial values are in fact the converged values
fm1 <- nls(weight ~ SSweibull(Time, Asym, Drop, lrc, pwr), data = Chick.6)
summary(fm1)
## Data and Fit:
plot(weight ~ Time, Chick.6, xlim = c(0, 21), main = "SSweibull() fit to Chick.6")
ux <- par("usr")[1:2]; x <- seq(ux[1], ux[2], length.out=250)
lines(x, do.call(SSweibull, c(list(x=x), coef(fm1))), col = "red", lwd=2)
As <- coef(fm1)[["Asym"]]; abline(v = 0, h = c(As, As - coef(fm1)[["Drop"]]), lty = 3)
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